CODES and CIPHERS
Нελλο, ωελχομε το ψουρ Ματηεματιχσ Χ ασσιγνμεντ. Τηισ ισ α φερψ εασψ χοδε, Ι ηοπε ψου χαν βρεακ ιτ.
P atiitg? Gtpaan, Sjbqatsdgt, ndj iwxcz ndj rpc tmeapxc paa iwxh xc p atiitg? Iwtht etdeat lxaa ctktg jcstghipcs wxb! Wt’aa qt upbdjh – p atvtcs – x ldjasc’I qt hjgegxhts xu idspn lph zcdlc ph Wpggn Ediitg spn xc ujijgt – iwtgt lxaa qt qddzh lgxiitc pqdji Wpggn – tktgn rwxas lxaa zcdl wxh cpbt!
CRYPTOLOGY or CRYPTOGRAPHY
Cryptology is an enormous field of study and its importance is rapidly increasing as security in digital communication becomes more and more vital for governments, business and industry and individuals. There are much more complicated ways of generating codes than those used above. Special machines have been designed (a well-known one is called “Enigma”) and matrix algebra can be used, as can random number generators.
Of course coded messages do have to be deciphered. The person who is meant to read the message must be able to make sense of it. Therefore it is just as important to have a decoding system that is easy to understand.
A good coding system must allow messages to be
- readily encoded by a sender who uses the key
- readily decoded by a recipient who knows the key
- difficult to crack if intercepted
present information appropriately, accurately and in an organised manner
Question 1 (3, 4 marks) Harry Potter and the Philosopher’s Code
Message 1 and Message 2 were coded using a very simple process. This type of coding mechanism is a straight-forward substitution of one character for another – called a substitution cipher. This code can be broken by working out the character representing each letter. If you know enough about the frequency of letters and the length of words then you can decipher the code fairly easily. Of course simple strategies such as regrouping the characters so that they are no longer in the word groupings would make the code harder to solve. (A one-letter word must be a or I, mustn’t it?)
Decode Message 1 and Message 2 and determine and explain the encryption keys used for each. Email a simple message to your email buddy using each of these encoding techniques. Print out the email you receive, decode it and include it in your submitted assignment.
Question 2 (5 marks) Harry Potter and the Chamber of Ciphers
Message 3 has been encoded with another type of cipher, made famous by Julius Caesar – called a Caesar Shift Cipher. In this encryption technique, each letter in a message is substituted with the letter that was a certain number of places further down the alphabet.
For example A B C D E F …
becomes C D E F G H …
so coded letter = original letter + 2.
Decode Message 3 and explain the equations used to encode and decode the message. Email a short simple message to your email buddy using this message encoding technique. Print out the email you receive, decode it and include it in your submitted assignment.
Question 3 (8 marks) Harry Potter and the Prisoner of Encryption
The cryptogram in Message 4 has resulted from a more complicated sort of Caesar Shift Cipher. As well as this, a space has been replaced by @ in the original message.
Message 4 was encrypted using a simple linear mathematical formula or equation. To do this you must first digitise the alphabet as follows: space (@) = 0, A = 1, B = 2, C = 3, … , Z = 26; the encrypting equation is then applied and the numbers converted back into letters. For example, I might apply my equation to the number 1, which represents A in the original message, and I obtain the number 20, which represents T then As in the original become Ts in the code.
Determine the encryption equation and the decryption equation used to encrypt and decrypt Message 4. You might be able to find a single equation that does both. Demonstrate, using 2 examples, how the equation works.
~ END OF PART A ~